5x^2+7x-22=0

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Solution for 5x^2+7x-22=0 equation: 


Simplifying
5x2 + 7x + -22 = 0

Reorder the terms:
-22 + 7x + 5x2 = 0

Solving
-22 + 7x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-4.4 + 1.4x + x2 = 0

Move the constant term to the right:

Add '4.4' to each side of the equation.
-4.4 + 1.4x + 4.4 + x2 = 0 + 4.4

Reorder the terms:
-4.4 + 4.4 + 1.4x + x2 = 0 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + 1.4x + x2 = 0 + 4.4
1.4x + x2 = 0 + 4.4

Combine like terms: 0 + 4.4 = 4.4
1.4x + x2 = 4.4

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 4.4 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 4.4 + 0.49

Combine like terms: 4.4 + 0.49 = 4.89
0.49 + 1.4x + x2 = 4.89

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 4.89

Calculate the square root of the right side: 2.211334439

Break this problem into two subproblems by setting 
(x + 0.7) equal to 2.211334439 and -2.211334439.


Subproblem 1
x + 0.7 = 2.211334439

Simplifying
x + 0.7 = 2.211334439

Reorder the terms:
0.7 + x = 2.211334439

Solving
0.7 + x = 2.211334439

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = 2.211334439 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 2.211334439 + -0.7
x = 2.211334439 + -0.7

Combine like terms: 2.211334439 + -0.7 = 1.511334439
x = 1.511334439

Simplifying
x = 1.511334439


Subproblem 2
x + 0.7 = -2.211334439

Simplifying
x + 0.7 = -2.211334439

Reorder the terms:
0.7 + x = -2.211334439

Solving
0.7 + x = -2.211334439

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = -2.211334439 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -2.211334439 + -0.7
x = -2.211334439 + -0.7

Combine like terms: -2.211334439 + -0.7 = -2.911334439
x = -2.911334439

Simplifying
x = -2.911334439


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.511334439, -2.911334439}

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